Final answer:
At each recursive call of the algorithm described by the recurrence relation T(n) = 9T(n/3) + n, nine sub-problems are created, each of which is one-third the size of the original problem.
Step-by-step explanation:
The question is related to the analysis of a recursive algorithm based on its recurrence relation. The given recurrence relation T(n) = 9T(n/3) + n defines the behavior of the algorithm and specifically how many sub-problems it generates at each step. The relation indicates that at each recursive call, the problem is divided into 9 sub-problems, each of one-third the size of the original problem.
If we look at the recurrence relation: T(n) = 9T(n/3) + n, the term 9T(n/3) tells us that the algorithm splits the problem into 9 smaller problems of size n/3 in each recursive step. This corresponds to a divide and conquer strategy where the original problem is divided into a fixed number of smaller instances, which are then resolved recursively. The additional term + n represents the combination step where the results of the sub-problems are combined, with n typically representing the 'work' done at each level of recursion besides dividing the problem.